STANDARDS AT GCSE

In this section we look briefly at the interface between GCSE and A-level. The most immediate question is:

• Are current standards in mathematics at GCSE (Grades A--C) in any way comparable to those associated with GCE O-level and CSE (Grade 1)?

The percentages of students obtaining Grades A to C have risen sharply in the last decade, and there would seem to be clear evidence of grade dilution. This and other structural changes have had a marked effect on the `gap' between GCSE and A-level. Since 1994 students can routinely obtain a Grade B taking only the intermediate tier GCSE papers, which assess students on a reduced syllabus (requiring, for example, very little algebra). Moreover, the mathematical knowledge now required to obtain an A* on GCSE papers in no way corresponds to that needed to obtain a good grade on the GCE additional mathematics formerly taken by many mathematically high-attaining students.

The difficulties such changes can cause are illustrated in the Engineering Council report (1994) [9] which describes the serious problems faced in higher education by students who obtain a Grade C in GCSE mathematics. Now, as a result of the change in grading procedures on the intermediate tier papers, such problems will be exacerbated. That change, like so many others, was made without a proper consideration of the consequences. Some attempts to avoid the more extreme abuses may have been introduced this year, but underlying issues, including comparability with other subjects, have still to be addressed, and the matter needs urgent review.

It is important to try to achieve some sort of consensus among professionals --- academics in mathematics, science and engineering, teachers in schools and colleges, educationalists and administrators --- as to the way forward. We cannot expect complete agreement on the extent to which standards have changed. However, few would dispute the observations that:

(a)

in recent years less emphasis has been placed on the acquisition of skills involving arithmetic, fractions, ratios, algebraic technique, and the basic geometry of triangles, lines and circles;

(b)

all of these neglected topics are vital for further study in mathematics, science and engineering.

At the same time we have seen greatly increased dependence upon calculators and computers. These are invaluable tools which have a place in the mathematics classroom; but their advent does not greatly change the mathematics which beginners need to master --- a fact which is reflected in the relatively conservative mathematics curricula of those countries with the strongest commitment to modern technology. Nor does it mean that pupils need no longer achieve fluency in traditional written methods. This applies especially when laying key numerical or algebraic foundations with beginners. Therefore, while we welcome the review of calculator usage to be carried out by SCAA, we urge that it should not be restricted to short- term effects on arithmetical competence, but that the experiences of those in higher education should be sought to try to assess how typical uses of calculators in schools have affected students' long-term mathematical thinking and behaviour.

We need an urgent and serious examination of what levels of `traditional' numerical and algebraic fluency are needed as a foundation for students' subsequent mathematical progress, and how such levels of fluency can be reliably attained.